Finite Group DatabasebetaFinite Group DatabasebetaOrder 14464.
520 conjugacy classes of subgroups; only the 137 normal subgroups are shown.
This group has 520 conjugacy classes of subgroups — too many to draw. Only its 137 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#16813596 | C2 | semidirect |
| 2. #20298912 | C2 | semidirect |
| 3. #20298834 | C2 | semidirect |
| 4. #20298734 | C2 | semidirect |
| 5. C2×C22⋊C8×C113 | C2 | semidirect |
| 6. C22×D452 | C22 | semidirect |
| 8. C2×D904 | C22 | semidirect |
| 12. #16813596 | C22 | semidirect |
| 13. C2×C4⋊Dic113 | C22 | semidirect |
| 15. #16813556 | C22 | semidirect |
| 16. #16813544 | C22 | semidirect |
| 18. C22×C8×C113 | C22 | semidirect |
| 19. C22⋊C8×C113 | C22 | semidirect |
| 43. C23×C113 | D8 | semidirect |
| 87. C113 | #3186 | semidirect |
| 92. C2×C22⋊C8 | D113 | semidirect |
| 97. C22×C8 | C2×D113 | semidirect |
| 106. C22⋊C8 | C2×D113 | semidirect |
| 134. C23 | D904 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16813596 | 2 |
| #20298912 | 2 |
| #20298834 | 2 |
| #20298734 | 2 |
| C2×C22⋊C8×C113 | 2 |
| #3186 | 113 |